Problem in mechanics

1. The problem statement, all variables and given/known data
A race car starts from rest on a circular track. the car increases its speed at a constant rate at as it goes once around the track.

2. Relevant equations

Find the angle that the total acceleration of the car makes- with the radius connecting the centre of the track and the car- at the moment the car completes the circle.

3. The attempt at a solution
First I put the angle = [tex]\theta[/tex]
I put the total acceleration = a
and ar= a radial
and then I found that Cos[tex]\theta[/tex]=[tex]\frac{a r }{a}[/tex]
then I said ar=[tex]\frac{v2}{r}[/tex]
and v2=[tex]\frac{2 by r}{T}[/tex] where T is the period. But I stopped I have no numbers
So can any one help me?

Staff: Mentor

Do this: Call the tangential acceleration at. Use this to figure out the speed at the end of circle and thus ar. Use those components to find the angle. (Hint: Express everything in terms of the final speed and the radius.)

Do this: Call the tangential acceleration at. Use this to figure out the speed at the end of circle and thus ar. Use those components to find the angle. (Hint: Express everything in terms of the final speed and the radius.)

hey Doc Al am just typing the answer to make sure it is okay, cause I think there is something error because the final answer unreasonable
This what I have done
since at=[tex]\frac{Vf2}{2\pi r}[/tex]
and ar=[tex]\frac{vf2}{r}[/tex]
therefore tan[tex]\theta[/tex]= [tex]\frac{at}{ar}[/tex]
therefore tan[tex]\theta[/tex]= [tex]\frac{v2}{4\pi r}[/tex] × [tex]\frac{r}{v2}[/tex]
So [tex]\theta[/tex] = tan-1([tex]\frac{1}{4 \pi}[/tex]
So [tex]\theta[/tex] = 4.548 degrees
I think the angle is too small and it is incorrect !! ?